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Theorem fneq2d 4933
Description: Equality deduction for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
fneq2d.1 (φA = B)
Assertion
Ref Expression
fneq2d (φ → (𝐹 Fn A𝐹 Fn B))

Proof of Theorem fneq2d
StepHypRef Expression
1 fneq2d.1 . 2 (φA = B)
2 fneq2 4931 . 2 (A = B → (𝐹 Fn A𝐹 Fn B))
31, 2syl 14 1 (φ → (𝐹 Fn A𝐹 Fn B))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1242   Fn wfn 4840
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-fn 4848
This theorem is referenced by:  fneq12d  4934
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